Write the equation of a line that is parallel to ${y=-0.75x}$ and that passes through the point ${(8,0)}$.
Solution: Getting started Key idea: Parallel lines have the same slope. Step 1: Find the slope Slope of the given line: ${-0.75}$ Slope of the parallel line: $C{-0.75}$ Step 2: Substitute the known point into linear equation The parallel line will have a slope of $C{-0.75}$ and pass through the point ${(8,0)}$. Let's start from the point-slope form of the equation of the parallel line, then solve for $y$. [What is the point-slope form?] $\begin{aligned} y-{0} &= C{-0.75}(x-{8})\\\\\\ y &= C{-0.75}x {+6} \end{aligned}$ Answer The equation of the parallel line is $y = C{-0.75}x {+6}$. ${2}$ ${4}$ ${6}$ ${8}$ ${\llap{-}4}$ ${\llap{-}6}$ ${\llap{-}8}$ ${2}$ ${4}$ ${6}$ ${8}$ ${\llap{-}4}$ ${\llap{-}6}$ ${\llap{-}8}$ $y$ $x$